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1.- Originally, fdisk created partitions trying to make them aligned to cylinder boundaries, leaving the first cylinder on disk free, as it would be used for the MBR, patition table and other stuff. This way, the first partition usually started on block 63 (each block being 512 bytes). The fdisk from distributions like RedHat 6.x, still works this way, but ...

I suggest that you immediately make a mirror of the damaged drive to avoid losing any more information. Your hardware is most likely bad and I would not mess with it further unless you like frustration.
You can try to recover the image after restoriing it to a new disk. But I'm betting unless the data is extremely important that will be a time ...

By some mystery I had wiped the volume group and the physical volume in it. It was just a matter of recovering them using the metadata I could back-up using testdisk. I copied the original /etc/lvm folder on the Desktop of the live user, then
$ pvcreate --uuid "cZ83jX-WXkk-tNG4-ulGT-sAqq-HlKq-Omtqc8" \
--restorefile ...

The resize_inode feature creates a hidden inode ( number 7, you can view it in debugfs with stat <7> ) to reserve those blocks so that the GDT can be grown. By default it reserves enough space to grow the filesystem to 1024 times its original size. You can disable the feature or adjust the size using options to mke2fs at format time.
What does ...